When a test contains a number of sections or subtests, each having been taken by the exact same sample of candidates who took that test, one may wish to know what each section contributes to whatever the test is primarily measuring. The crudest way to achieve this is to compute the correlation of each section with total score on the test. A more refined way is to extract the "first factor" from the correlation matrix consisting of all the intercorrelations of the sections/subtests, including the correlations of the sections with themselves (that is, their reliability coefficients).
The reliability of a section or subtest can either be computed internally with the split-half method or Crohnbach's alpha, or estimated by taking, for each section, the highest of its significant correlations with the other sections. The latter is reasonable because a section can not correlate higher with any other section than it correlates with itself. Although self-obvious, it is pointed out that the number of candidates having taken the test should be sufficient for these section intercorrelations to become significant.
For each section, its correlations and reliability are summed. In case of a four-section test, this means to sum four numbers, for instance. Then, the sums of the sections are summed into a total sum. Then, for each section, its loading on the first factor is computed as [the sum of that section] divided by [the square root of the total sum]. So:
Loadingsection = Sumsection / √(Total sum)
Finally, the proportion of total test score variance accounted for by the first factor is computed as [the sum of squares of the sections' loadings] divided by [the number of sections]. So:
Proportion of variance accounted for = Σ(Loadingsection)2 / (Number of sections)
Notice that the first factor in any test's variance is not necessarily the g factor, although when all sections/subtests deal with some mental ability it will likely be related to the g factor. When all or most of the sections deal with non-cognitive traits or skills, one may theoretically expect the first factor to be non-g. The remainder of test score variance (apart from the first factor) may consist of (other) group factors (common to some but not all sections), specificity (unique to one particular section), or error.
To further clarify the difference between the "first factor" and the g factor: The latter accounts for that part of the variance that is common to all tests dealing with mental abilities. The former is just the factor that accounts for more variance than do any other factors in a given matrix of intercorrelations, regardless of the question whether or not it (the first factor) is shared by all of the tests/sections in that matrix, and regardless of the nature of the tests/sections (cognitive or non-cognitive). Emphatically, one should realize that the presence of the g factor in any matrix of intercorrelations is not a priori required! A matrix without the g factor is entirely possible. The g factor found among mental tests is an unexpected empirical phenomenon, not an a priori theoretical supposition.
A reasonable convention in the context of high-range testing is to reserve the term "(conservatively estimated) g factor loading" for the analysis of a test's correlations with a large number of other intelligence tests. The first factor found among the (small number of) sections or subtests of a particular test should simply be called "first factor" without claiming identity with the g factor.